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National and Regional Contests
Nigeria Contests
Nigerian Senior Mathematics Olympiad Round 2
2022 Nigerian Senior MO Round 2
Problem 3
Problem 3
Part of
2022 Nigerian Senior MO Round 2
Problems
(1)
Real lengths?
Source: 2022 Nigerian Senior MO Round 2/Problem 3
5/6/2022
In triangle
A
B
C
ABC
A
BC
,
A
D
AD
A
D
and
A
E
AE
A
E
trisect
∠
B
A
C
\angle BAC
∠
B
A
C
. The lengths of
B
D
,
D
E
BD, DE
B
D
,
D
E
and
E
C
EC
EC
are
1
,
3
1, 3
1
,
3
and
5
5
5
respectively. Find the length of
A
C
AC
A
C
.
geometry
complex numbers
imaginary triangle